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美国大学生数学建模大赛2009年MCM特等奖论文.doc

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PoliticalAdvertisingBudgetingforObama2012Re-electionSummaryTospecifytheproblem,weconsiderthesituationtheObamacampaignmeetstoprepareforthe2012re-election.Thetotal91millionUSdollarscampaignfundsisdistributedtotwoaspects：thenewmediaInternetandpoliticalactivities.WeusetheAnalyticalHierarchyProcessmethodtoobtaintheinvestmenttheObamacampaignshouldpourintothemajorInternetcompanies.Theweighteachcompanyownsisinproportionaltotheexpenditurethecampaignspentonthemin2008.Weconcludethatatotal7millionUSdollarsshouldbepreparedfortheInternet,ofwhich5millionisdirectlyspentandtheremaining2millionincrementalbudgetingisforspecialsituations.Asforthepoliticalactivities,thenumberofelectoralvotesawardedtoeachstateisthemainfactorinourmodel.Consideringthepreviouselections,therearestatestendtosupporttheDemocraticPartyortheRepublicanParty.ThisisrelativelyconvenientforustomodeltheexpendituredistributedtoeachstatebecausesomestatesareofsmallprobabilityfortheDemocraticPartytofightfor.Wedonottakeintoaccountthe8stateswhichstronglysupporttheRepublicanPartyinpreviouselections.Intheremaining42statesandtheDist.ofColumbia,wedesignarank-orientedmethodtodistributetheremaining84milliondollars;thearrangementforeachstateispresentedinthispaper.1IntroductionIntheUShistory,eachcandidatehasaelectoralteamaimedatwinningthebattleforthepresidentialelection.Beforetheprimaryelection,teammemberswillcollectalargeamountofinformationtoanalyzetheelectoralsituationofeverystatesoastoknowthemeasurestheyshouldtakeineachstaterespectively.Consideringaspecificstate,whetheritappliestheproportionalorthe“winner-takes-all”systemaffectstheelectiongreatly.Howtospendthecampaignfundsdependtoalargeextentonthenumberofelectoralvotesawardedbythestate.Tobespecific,weassumethecandidatetobetheincumbentUSpresidentBarackHusseinObamaandbudgetthecampaignfundsforhis2012re-election.SinceObamarepresentstheDemocraticParty,ourmodelaimsathelpingtheObamacampaignwinthebattleagainsttheRepublicanParty.Inthelasttenelections,4statesof56electoralvotessupporttheDem